The Micro Exporter (which is exclusive to Professional versions), which is used to export terrain as an object, is in its infancy currently. It does not support texture export. You can do this separately by doing an ortho export of the terrain, and an ortho export of the terrain colour with same dimensions. Note that this method doesn't work well with very steep cliffs, as your exported texture will probably stretch in those areas. It also cannot capture texture under overhangs. Some things to consider.
Matt is working on texture exporting, and we can hope to see that in the future.